Question

What will come in place of the question mark in the following numerical series?
6, 9, 14, 21, 30, ?

• A. 36
• B. 41
• C. 62
• D. 59

Hint:

When faced with a number series, always start by checking the differences between consecutive terms. If the first-level differences don't show a clear pattern, check the differences of the differences (second-level differences).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a number series problem where we need to identify the pattern governing the sequence of numbers to find the next term.
Step 2: Key Formula or Approach:
A common method to find the pattern is to calculate the difference between consecutive terms.
Step 3: Detailed Explanation:
Let's find the difference between each pair of consecutive numbers in the series:

\(9 - 6 = 3\)
\(14 - 9 = 5\)
\(21 - 14 = 7\)
\(30 - 21 = 9\)
The differences are 3, 5, 7, 9. This is a sequence of consecutive odd numbers.
The next odd number in this sequence will be 11.
To find the next term in the original series, we add this difference to the last term (30).
Next term = \(30 + 11 = 41\).
Step 4: Final Answer:
The number that will come in place of the question mark is 41.